China has evacuated more than 3,000 of its nationals from Vietnam, state media reported on Sunday, after a wave of anti-China unrest following Beijing's deployment of an oil rig in contested waters.

But the anti-China protests planned for Sunday in Ho Chi Minh City, originally sanctioned by the Vietnamese government, were quickly stopped by scores of uniformed and secret police.

Armed with batons and walkie talkies, they contained the small group of protesters holding up notebook-sized banners reading "Vietnam is small but no coward" and chanting "Vietnam! Vietnam!".

About 15-20 demonstrators were seen to be detained and pushed into unmarked vans.

The government has been sending daily text messages to all mobile phone users in Vietnam, urging them to exercise restraint and not engage in violent behaviour. The latest message, sent on Sunday, warned citizens against joining in the planned protests.

The Vietnamese government is obviously keen to control the situation – Chinese-Vietnamese trade is worth some $50b – but much of the damage may have already been done. In Ho Chi Minh City's Chinese-majority District 5, shopkeepers have begun dismantling, or covering up, any Chinese characters on their storefronts, out of fear that the anti-China aggression may turn directly on them.

"The government sent us a letter telling us to do this," said Van Vuy, the manager of a silkscreen-printing business. "I don't want to, but the owner is scared of what might happen if we don't."

The Chinese government was also arranging for a chartered plane and vessel to evacuate the staff of China 19th Metallurgical Corporation, a contractor of one of the plants badly hit by the recent violence, Agence France-Presse reported, citing Xinhua.

In a later update the agency reported: "Sixteen critically injured Chinese nationals were evacuated from Vietnam early on Sunday morning aboard a chartered medical flight arranged by [the] Chinese government."

It did not specify which company they were working for.

On Sunday China dispatched a further five ships to speed up the evacuation of its citizens, the Associated Press reported. The first ship left on Sunday morning from the southern island of Hainan, Xinhua said.

Beijing on Saturday advised its nationals against travelling to Vietnam, which has seen its worst anti-China unrest in decades over the past week, AFP reported.

China's positioning of an oil rig in waters also claimed by Vietnam in the South China Sea has ignited long-simmering enmity between the two communist neighbours.

Demonstrations spread to 22 of Vietnam's 63 provinces in the last week, according to the Vietnamese government, with enraged mobs torching foreign-owned factories.

Hong Kong also updated its travel advisory on Saturday, warning its residents to avoid "non-essential travel" to Vietnam.

On Saturday Xinhua reported that security chief Guo Shengkun had spoken to his Vietnamese counterpart and urged the authorities there to quell the violence. Xinhua also said commerce minister Gao Hucheng had called on officials to "bring relevant issues under control".

An alliance of 20 vocal Vietnamese NGOs has called for fresh protests in Hanoi, Ho Chi Minh City and other areas against China's "aggressive actions" in the South China Sea.

However, it urged participants to remain peaceful following the chaos on Tuesday and Wednesday.

"Those violent actions created a bad image for patriotic demonstrations and the people of Vietnam; therefore, they must be stopped," said a statement issued on social media late on Friday.

The alliance largely comprises anti-government organisations and is believed to have played a role in stirring the recent protests.

The oil-rig confrontation is the latest to spark alarm among China's south-east Asian neighbours, which complain of increasing maritime intimidation by Beijing.

China claims nearly all of the South China Sea, which is believed to hold significant offshore energy reserves.